In terms of cold packing materials, sealed ice packs of water ice are rarely a problem in the hold. Restrictions apply to various cold-gas systems like dry ice, liquid nitrogen, etc.
The standard packaging bubble wrap is both good cushioning and an excellent insulator. In this sort of situation I would place some ice packs, if I could get them, next to the item to be chilled and wrap it all in layers (several cm thick in total) of bubble wrap. Tape the edges closed and place the package in the center of your luggage.
It can be helpful to tape the closure of the bottle to ensure it does not work its way open in flight. An impromptu ice pack can be created by freezing a small plastic bottle of water - do tape the closure of that bottle too!